Early Papers on Interval Computations

Origins of Interval Computations: from Archimedes to 1960s

Archimedes, "On the measurement of the circle", In: Thomas L. Heath (ed.), The Works of Archimedes, Cambridge University Press, Cambridge, 1897; Dover edition, 1953, pp. 91-98.

W. H. Young, "Sull due funzioni a piu valori constituite dai limiti d'una funzione di variable reale a destra ed a sinistra di ciascun punto", Rendiconti Academia di Lincei, Classes di Scienza Fiziche, 1908, Vol. 17, No. 5, pp. 582-587.

R. C. Young, "The algebra of multi-valued quantities", Mathematische Annalen, 1931, Vol. 104, pp. 260-290.

P. S. Dwyer, Linear Computations, J. Wiley, N.Y., 1951.

M. Warmus, "Calculus of Approximations", Bulletin de l'Academie Polonaise de Sciences, 1956, Vol. 4, No. 5, pp. 253-257; see also a nice quality version

M. Warmus, "Approximations and Inequalities in the Calculus of Approximations. Classification of Approximate Numbers", Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys., 1961, Vol. 9, pp. 241-245.

T. Sunaga, "Theory of interval algebra and its application to numerical analysis", In: Research Association of Applied Geometry (RAAG) Memoirs, Ggujutsu Bunken Fukuy-kai. Tokyo, Japan, Vol. 2, 1958, pp. 29-46 (547-564).

For an early history of interval computations, see also

S. Markov and K. Okumura, "The Contribution of T. Sunaga to Interval Analysis and Reliable Computing", In: T. Csendes (ed.), Developements in Reliable Computing, Kluwer, Dordrecht, 1999, pp. 167-188.

Selected Papers from the 1970s and 1980s

• Karl Nickel, On the Newton method in interval analysis, MRC Rechnical Summary Report #1136, University of Wisconsin, Madison, 1971.

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